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Friday, July 31, 2020 | History

5 edition of Hopf algebras and quantum groups found in the catalog.

Hopf algebras and quantum groups

proceedings of the Brussels conference

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Published by Marcel Dekker in New York .
Written in English

    Subjects:
  • Hopf algebras -- Congresses.,
  • Quantum groups -- Congresses.

  • Edition Notes

    Statementedited by Stefaan Caenepeel, Freddy Van Oystaeyen.
    GenreCongresses.
    SeriesLecture notes in pure and applied mathematics ;, 209, Lecture notes in pure and applied mathematics ;, v. 209.
    ContributionsCaenepeel, Stefaan, 1956-, Oystaeyen, F. van, 1947-, Université libre de Bruxelles.
    Classifications
    LC ClassificationsQA613.8 .H67 2000
    The Physical Object
    Paginationxii, 309 p. :
    Number of Pages309
    ID Numbers
    Open LibraryOL6897841M
    ISBN 100824703952
    LC Control Number00701280
    OCLC/WorldCa44164607

    The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.5/5(1). The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author's publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course.

    I start with self study about quantum groups. Until now I covered Hopf $*$-algebras and there representations (for example by the book of Klymik and Schmüdgen). Now I want to understand the step from Hopf algebras to quantum groups (and especially to compact quantum groups). Quantum Groups and Hopf Algebras. Article (PDF Available) April 2 This book gives a comprehensive view of quantum groups and their applications. The authors build on a self-contained Author: Gastón Andrés García.

      On quasitriangular quasi-Hopf algebras and a group closely connected with(ℚ/ℚ, Algebra Anal. 2 no. 4 (), – (in Russian) MathSciNet Google Scholar. This work very nicely complements the other texts on Hopf algebras and is a welcome addition to the literature.” —Jan E. Grabowski, Mathematical Reviews, July, "In this book, Underwood chooses to introduce Hopf algebras in a manner most natural to a reader whose knowledge of algebra does not extend much beyond a first year graduate.


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Hopf algebras and quantum groups Download PDF EPUB FB2

Hopf Algebras, Quantum Groups and Yang-Baxter Equations by Florin Felix Nichita (ed.). Publisher: MDPI AG ISBN Number of pages: Description: Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are presented in this volume.

This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers Hopf algebras and quantum groups book selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum groups.

This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum gAuthor: Stefaan Caenepeel, Freddy Van Oystaeyen.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations. Florin Felix Nichita (Ed.) Pages: Published: January (This book is a printed edition of the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations that was published in Axioms) Download PDF.

Add this book. Foundations of Quantum Group Theory, by Shahn Majid. Goes into more detail on braided monoidal categories, braided Hopf algebras, reconstruction theorems (i.e. reconstructing a Hopf algebra from its category of representations) than most other books, although some of this is covered in Chari-Pressley.

Quantum Groups, by Christian Kassel. The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.

This textbook presents the second edition of Manin's celebrated Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense.

The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. By relating the diagrammatic foundations of knot theory with the structure of abstract tensors, quantum groups and ribbon Hopf algebras, specific expressions are derived for quantum link invariants.

These expressions, when applied to the case of finite dimensional unimodular ribbon Hopf algebras, give rise to invariants of 3-manifolds. Apoorva Khare, in the article ”The Sum of a Finite Group of Weights of a Hopf Algebra”, evaluates the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements.

”Valued Graphs and the Representation Theory of Lie Algebras”, by Joel Lemay, deals with. This book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on Drinfeld's recent fundamental contributions.

The first part presents in detail the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. is, Hopf algebras, algebraic, formal, and quantum groups. This is chapter 2 of his book Lectures on quantum groups and noncommutative geometry ein, Sackler lectures on quantum groups and TQFTs.A survey of quantum groups (gunzipped ps file)In and around the origin of quantum groups.

4. Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality. A New Proof of the Skolem-Noether Theorem. Projectivity of a Relative Hopf Module over the Subring of Coinvariants. A Brief Introduction to Coalgebra Representation Theory.

Some Examples of Integrals for Bialgebras. Bi-Frobenius Algebras and Group-Like. $\begingroup$ Nobody quite agrees what the correct answer is to the question "what is a quantum group", mainly because nobody has found a satisfying definition that includes all the Drinfeld-Jimbo examples without either being somewhat artificial (ie, defining the term to mean one of those examples), or including too many hopf-algebras.

However, the term "compact quantum group" has a. Quantum groups are not groups at all, but special kinds of Hopf algebras of which the most important are closely related to Lie groups and play a central role in the statistical and wave mechanics of Baxter and Yang.

Those occurring physically can be studied as essentially algebraic and closely related to the deformation theory of algebras (commutative, Lie, Hopf, and so on). Drinfeld–Jimbo type quantum groups. One type of objects commonly called a "quantum group" appeared in the work of Vladimir Drinfeld and Michio Jimbo as a deformation of the universal enveloping algebra of a semisimple Lie algebra or, more generally, a Kac–Moody algebra, in the category of Hopf resulting algebra has additional structure, making it into a quasitriangular Hopf.

In the rest of the book we learn many facts and constructions related to the theory of quantum groups as studied by operator algebraists. A C * structure is added to the Hopf algebra structure, and the quantum groups that are described and studied are assumed to mostly be function algebras and their generalizations.

Due to this focus, the dual. Quantum Groups. This class meets Mondays and Wednesdays in I. Lecture 1. Introduction. Bialgebras. Hopf Algebras. Examples of Hopf Algebras. Lecture 2. Sweedler notation. Bialgebras and monoidal categories. Rigid categories. Braided monoidal categories.

Lecture 3. Braided categories. Quasitriangular Hopf algebras. Quantized. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras.

This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than.

It gives an interpretation of quantum groups in the setting of C*-algebras and von Neumann algebras. The compact case (developed by Woronowicz) is included as a special case.

This book is devoted to a description of this theory. It has three parts. The first part treats quantum groups (and their duality) in a purely algebraic setting. Lead by examples we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vectorfields).

The examples of the quantum sl(2) Lie algebra and of the quantum (twisted) Poincare Lie algebra iso_θ(3,1) are presented.The author investigates in detail the quantum group SLq(n), which is based on the classical Lie group.

References are given for quantum groups based on the other Lie groups, such as the orthogonal and symplectic groups. The Lie algebra Uq(sl(2)) is given a detailed treatment by the author when q is not a root of unity.

This Hopf algebra is a 1 Reviews: 3.Drinfeld's original ICM talk "Quantum groups" is something "must read", scanned files are available here. This old introduction works out many details and is quite good: "An introduction to quantized Lie groups and algebras" arXiv:hep-th/ There is certain interplay between certain topics in classical simple Lie algebras and quantum groups, in particular the Yangian.